2023 · Q4
If the roots of the equation x² - bx + c = 5 differ by 5, then which one of the following is correct?
Elementary MathematicsAlgebra
- Ab² = 4c + 5
- Bc² = 4b - 5
- Cb² + c² = 5
- Db² - c² = 5
Explanation
Rewriting gives x² − bx + (c − 5) = 0 with roots r₁, r₂ satisfying |r₁ − r₂| = 5. Then (r₁ − r₂)² = (r₁ + r₂)² − 4r₁r₂ = b² − 4(c − 5) = 25. Simplifying yields b² = 25 + 4c − 20 = 4c + 5 (A).